When the two vortices in a vortex pair approach each, then a second
regularization becomes necessary. If one does not want the two vortices to just annihilate each other
in the limit, then one has to let the strengths of the vortices tend to infinity. Even without that, the speed of the vortex
pair will be infinite in the limit, so with the vortex strengths blowing up the speed will become infinite to an even higher degree.
But in any case one can speak of a residual trajectory, which will be a geodesic for the metric of the manifold, as was conjectured in
[1]}, proved in [2]}, and further clarified in Theorem REF  above.
